A309312 Areas of Heronian triangles that uniquely define the lengths of the triangle's sides.

6, 30, 42, 54, 66, 72, 114, 132, 150, 198, 204, 234, 294, 306, 378, 390, 408, 468, 486, 522, 570, 594, 648, 684, 726, 744, 750, 798, 816, 876, 984, 1014, 1026, 1110, 1170, 1218, 1254, 1290, 1332, 1350, 1368, 1428, 1494, 1518, 1548, 1554, 1590, 1734, 1770, 1782, 1806, 1938, 1950, 1974

Offset

1,1

Comments

These are not necessarily primitive Heronian triangles. The corresponding sequence for primitive Heronian triangles is neither a subset nor a superset of this sequence.

Links

Giovanni Resta, Table of n, a(n) for n = 1..10000 (first 500 terms from Jacob Vecht)

Wikipedia, Heronian triangle

Example

A triangle with integer sides and an area of 42 square units necessarily has sides 7,15,20, so 42 is a term. 12 is not a term because an area of 12 could have sides 6,5,5 or 8,5,5.

Crossrefs

Subsequence of A188158.

Sequence in context: A003062 A327157 A336216 * A101937 A101939 A290466

Adjacent sequences: A309309 A309310 A309311 * A309313 A309314 A309315

Keyword

nonn,easy

Author

Jacob Vecht, Jul 22 2019

Extensions

Corrected 37th term "1248" to "1254".

Status

approved